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Abstract: . We consider second-order differential systems where high-frequency oscillations are generated by a linear part. We present a frequency expansion of the solution, and we discuss two invariants of the system that determines the coefficients of the frequency expansion. These invariants are related to the total energy and the oscillatory harmonic energy of the original system. For the numerical solution we study a class of symmetric methods that discretize the linear part without error. We are... (Update)
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BibTeX entry: (Update)
E. Hairer and Ch. Lubich, Long-time energy conservation of numerical methods for oscillatory differential equations, Report, 1999, submitted to SIAM J. Numer. Anal. http://citeseer.ist.psu.edu/355435.html More
@article{ hairer01longtime,
author = "Ernst Hairer and Christian Lubich",
title = "Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations",
journal = "SIAM Journal on Numerical Analysis",
volume = "38",
number = "2",
pages = "414--441",
year = "2001",
url = "citeseer.ist.psu.edu/355435.html" }
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6 Long-time-step methods for oscillatory differential equation.. - Garc'ia-Archilla, Sanz-Serna et al. - 1999
5 Numerical integration of ordinary differential equations bas.. (context) - Gautschi - 1961
2 the problem of energy equipartition for large systems of the.. (context) - Galgani, Giorgilli et al. - 1992
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